An LNG reserve dispensing system and method
By using level sensors, pressure sensors, and data acquisition modules in LNG storage facilities, combined with price difference index and dynamic cost data, the timing and quantity of LNG release from storage facilities can be scientifically determined, solving the problem of inaccurate release in existing technologies and achieving multi-objective optimization and improved economic efficiency.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-11-24
- Publication Date
- 2026-04-07
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Figure CN117646867B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of LNG storage facilities, and in particular to an LNG storage and delivery system and method. Background Technology
[0002] Currently, China has basically established a natural gas reserve system with natural gas supply companies as the assessment units. However, because this system lacks detailed restrictions on the geographical location of the indicators, mismatches between reserve capacity and market demand frequently occur in practice.
[0003] In addition, there are multiple objectives to consider when to release reserve resources. However, current methods are often simplistic and crude, which leads to a high degree of subjectivity in decision-making. There is a large room for manipulation, such as exaggeration or underestimation, resulting in generally unsatisfactory resource supply and inaccurate timing or quantity of LNG reserve facility releases. Summary of the Invention
[0004] To address the aforementioned problems, the purpose of this invention is to provide an LNG storage and delivery system and method that can improve the accuracy of LNG storage facility delivery time or delivery volume.
[0005] To achieve the above objectives, the present invention adopts the following technical solution: On the one hand, it provides an LNG storage and release system, including a liquid level sensor, a pressure sensor, a data acquisition module, an LNG storage facility decision-making module, and an LNG storage facility operation module;
[0006] The liquid level sensor is used to collect the liquid level signal of the corresponding LNG receiving station storage tank in the LNG storage facility in real time. When the collected liquid level signal is less than the preset liquid level threshold, it outputs the demand signal of LNG storage quantity.
[0007] The pressure sensor is used to collect the pressure signal at the corresponding distribution station in real time. When the collected pressure signal is less than the preset pressure threshold, it outputs the LNG reserve demand signal.
[0008] The data acquisition module is used to acquire in real time the LNG price difference index of the pipeline network in the area covered by the LNG storage facility and the dynamic cost data of the LNG storage facility.
[0009] The LNG storage facility decision module is used to determine the release time and release quantity of the LNG storage facility, and to issue release instructions based on the LNG storage quantity demand signal sent by the liquid level sensor, the LNG storage quantity demand signal sent by the pressure sensor, the LNG price difference index of the regional pipeline network, or the dynamic cost data of the LNG storage facility.
[0010] The LNG storage facility operation module is used to control the LNG storage facility to release a determined amount of LNG into the regional pipeline network at a determined release time, according to the issued release instruction.
[0011] Furthermore, several of the liquid level sensors are fixedly installed at the corresponding LNG receiving station storage tanks within the corresponding LNG storage facilities, and several of the pressure sensors are fixedly installed at the corresponding distribution stations of the pipeline network covering the area of the LNG storage facilities.
[0012] Furthermore, the data acquisition operations of the liquid level sensor, pressure sensor, and data acquisition module are all based on the data acquisition demand signals periodically issued by the LNG storage facility decision module.
[0013] Furthermore, the LNG storage facility decision-making module is equipped with:
[0014] The data acquisition unit is used to acquire the demand signal of LNG reserves sent by the liquid level sensor or pressure sensor, as well as the LNG price difference index and dynamic cost data acquired by the data acquisition module.
[0015] The scheme determination unit is used to pre-determine the release time and quantity of LNG storage facilities;
[0016] The threshold setting unit is used to preset the price difference index threshold and the dynamic cost threshold;
[0017] The data processing unit is used to output a demand signal for LNG reserves when the LNG price difference index of the regional pipeline network is greater than the price difference index threshold, and to output a demand signal for LNG reserves when the dynamic cost data of the LNG storage facility is less than the dynamic cost threshold.
[0018] When the instruction issuing unit receives the LNG reserve demand signal from the liquid level sensor, the LNG reserve demand signal from the pressure sensor, or the LNG reserve demand signal output by the data processing unit, it issues a release instruction to the LNG storage facility operation module.
[0019] Furthermore, the LNG storage facility decision-making module is also equipped with:
[0020] The demand signal transmission unit is used to periodically output data acquisition demand signals to the liquid level sensor, pressure sensor and data acquisition module.
[0021] Furthermore, the LNG storage facility decision-making module is also equipped with:
[0022] The evaluation unit is used to periodically evaluate the resource allocation and acquisition operations within a certain time period based on actual needs.
[0023] On the other hand, a method for releasing LNG reserves is provided, including:
[0024] The data acquisition module obtains in real time the LNG price difference index of the pipeline network in the area covered by the LNG storage facility and the dynamic cost data of the LNG storage facility;
[0025] The LNG storage facility decision-making module determines the timing and quantity of LNG release from the storage facility;
[0026] Each level sensor collects the level signal of the corresponding LNG receiving station tank in the LNG storage facility in real time, and each pressure sensor collects the pressure signal of the corresponding distribution station in real time.
[0027] When the liquid level signal collected by the liquid level sensor is lower than the preset liquid level threshold, the demand signal for LNG storage is output to the LNG storage facility decision module.
[0028] When the liquid level signal collected by the liquid level sensor is not less than the preset liquid level threshold and the pressure signal collected by the pressure sensor is less than the preset pressure threshold, the demand signal for LNG storage quantity is output to the LNG storage facility decision module.
[0029] The LNG storage facility decision-making module issues a release instruction to the LNG storage facility action module based on the LNG storage demand signal sent by the level sensor, the LNG storage demand signal sent by the pressure sensor, the LNG price difference index of the regional pipeline network, or the dynamic cost data of the LNG storage facility.
[0030] The LNG storage facility operation module controls the LNG storage facility to release a predetermined amount of LNG into the regional pipeline network at a predetermined release time, based on the release command issued.
[0031] Furthermore, the method also includes:
[0032] A corresponding liquid level sensor is installed at each LNG receiving station storage tank within each LNG storage facility, and a corresponding pressure sensor is installed at each distribution station of the pipeline network covering the LNG storage facility area.
[0033] Furthermore, the method also includes:
[0034] The LNG storage facility decision-making module periodically sends out data collection request signals;
[0035] The data acquisition work of the level sensor, pressure sensor, and data acquisition module is all based on this data acquisition requirement signal.
[0036] Furthermore, the LNG storage facility decision-making module, based on the LNG storage demand signal sent by the level sensor, the LNG storage demand signal sent by the pressure sensor, the LNG price difference index of the regional pipeline network, or the dynamic cost data of the LNG storage facility, issues a release instruction to the LNG storage facility action module, including:
[0037] The LNG storage facility decision-making module pre-sets price difference index thresholds and dynamic cost thresholds;
[0038] When the pressure signal collected by the pressure sensor is not less than the preset pressure threshold and the LNG price difference index of the regional pipeline network is greater than the price difference index threshold, the demand signal for LNG reserves is output.
[0039] When the LNG price difference index of the regional pipeline network is not greater than the price difference index threshold and the dynamic cost data of the LNG storage facilities is less than the dynamic cost threshold, a demand signal for LNG storage volume is output; otherwise, the status quo is maintained.
[0040] The LNG storage facility decision-making module issues a release instruction to the LNG storage facility action module based on the demand signal for LNG storage volume.
[0041] The present invention has the following advantages due to the adoption of the above technical solutions:
[0042] 1. This invention controls the release of a predetermined amount of LNG from LNG storage facilities into the regional pipeline network at a predetermined time, based on the release time and quantity of LNG from the LNG storage facilities, as well as the collected liquid level signals, pressure signals, LNG price difference index, and dynamic cost data. This effectively balances multiple objectives such as facility liquid level safety, energy market supply security, market price maintenance, and facility economics to achieve optimal results. The decision-making is scientific and highly operable, enabling the LNG strategic reserve system to achieve synchronous coordination with the local natural gas market and efficiently maintain the safe and stable operation of the local regional pipeline network system.
[0043] 2. Because the present invention is equipped with a data acquisition module, it can obtain the LNG price difference index of the pipeline network in the area covered by the LNG storage facility and the dynamic cost data of the LNG storage facility in real time, which can optimize decision-making in real time, ensure the minimum project cost, and improve the economic efficiency of the project.
[0044] In summary, this invention can be widely applied in the field of LNG storage facilities. Attached Figure Description
[0045] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts. In the drawings:
[0046] Figure 1 This is a schematic diagram of the system structure provided in an embodiment of the present invention;
[0047] Figure 2 This is a schematic diagram of a method flow provided in an embodiment of the present invention. Detailed Implementation
[0048] Exemplary embodiments of the invention will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the invention are shown in the drawings, it should be understood that the invention can be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of the invention and to fully convey the scope of the invention to those skilled in the art.
[0049] It should be understood that the terminology used herein is for the purpose of describing particular exemplary embodiments only and is not intended to be limiting. Unless the context clearly indicates otherwise, the singular forms “a,” “an,” and “described” as used herein may also include the plural forms. The terms “comprising,” “including,” “containing,” and “having” are inclusive and therefore indicate the presence of the stated features, steps, operations, elements, and / or components, but do not exclude the presence or addition of one or more other features, steps, operations, elements, components, and / or combinations thereof. The method steps, processes, and operations described herein are not construed as requiring them to be performed in a particular order described or illustrated unless the order of performance is explicitly indicated. It should also be understood that additional or alternative steps may be used.
[0050] Although terms such as first, second, third, etc., may be used in this document to describe multiple elements, components, regions, layers, and / or segments, these elements, components, regions, layers, and / or segments should not be limited by these terms. These terms may be used only to distinguish one element, component, region, layer, or segment from another. Unless the context clearly indicates otherwise, terms such as "first," "second," and other numerical terms used herein do not imply order or sequence. Therefore, the first element, component, region, layer, or segment discussed below may be referred to as the second element, component, region, layer, or segment without departing from the teachings of the exemplary embodiments.
[0051] The timing of LNG reserve resource release presents a multi-objective decision-making problem, but current methods are often simplistic and crude, leading to a high degree of subjectivity in decision-making and generally unsatisfactory resource supply assurance. The LNG reserve release system and method provided in this invention input LNG reserve facility level signals, regional pipeline pressure change signals, LNG price difference index, and dynamic cost data in batches and layers into the LNG reserve facility decision-making process, thereby determining the release time and quantity of LNG reserves. This improves the accuracy of LNG reserve facility release timing or quantity, maintaining the normal operation of reserve projects. This invention is particularly applicable to LNG receiving terminals along coasts, rivers, and railways.
[0052] Example 1
[0053] like Figure 1 As shown, this embodiment provides an LNG storage and release system, including a level sensor, a pressure sensor, a data acquisition module, an LNG storage facility decision-making module, and an LNG storage facility operation module.
[0054] Several liquid level sensors are fixedly installed at the corresponding LNG receiving station storage tanks within the corresponding LNG storage facility. They are used to collect the liquid level signals of the corresponding LNG receiving station storage tanks in the LNG storage facility in real time based on the data collection demand signals periodically issued by the LNG storage facility decision module. When the collected liquid level signal is less than the preset liquid level threshold, the sensor outputs the demand signal for LNG storage quantity.
[0055] Several pressure sensors are fixedly installed at the corresponding distribution stations of the pipeline network in the area covered by the LNG storage facility. They are used to collect the pressure signals at the corresponding distribution stations in real time based on the data collection demand signals periodically issued by the LNG storage facility decision module. When the collected pressure signal is less than the preset pressure threshold, the demand signal for LNG storage is output.
[0056] The data acquisition module is used to obtain the LNG price difference index of the pipeline network in the area covered by the LNG storage facility and the dynamic cost data of the LNG storage facility in real time, based on the data acquisition demand signals periodically issued by the LNG storage facility decision module.
[0057] The LNG storage facility decision-making module is used to determine the release time and quantity of LNG storage facilities, and to issue release instructions based on the demand signals of LNG storage quantity sent by the level sensor, the demand signals of LNG storage quantity sent by the pressure sensor, the LNG price difference index of the regional pipeline network, or the dynamic cost data of the LNG storage facility.
[0058] The LNG storage facility operation module is used to control the LNG storage facility to release a predetermined amount of LNG into the regional pipeline network at a predetermined release time, based on the issued release instruction.
[0059] It should be noted that each LNG storage facility includes several LNG receiving terminal storage tanks, and these LNG storage facilities are located near coastal LNG receiving terminals.
[0060] In a preferred embodiment, the regional network is, for example, an international economy, a country, or a regional area.
[0061] In a preferred embodiment, each level sensor and pressure sensor has a built-in chip for outputting a demand signal for LNG reserves when the collected level signal or pressure signal is less than a preset threshold.
[0062] In a preferred embodiment, the LNG storage facility decision-making module includes a demand signal transmission unit, a data acquisition unit, a scheme determination unit, a threshold setting unit, a data processing unit, an instruction issuance unit, and an evaluation unit.
[0063] The demand signal transmission unit is used to periodically output data acquisition demand signals to the level sensor, pressure sensor, and data acquisition module.
[0064] The data acquisition unit is used to acquire the demand signal of LNG reserves sent by the liquid level sensor or pressure sensor, as well as the LNG price difference index and dynamic cost data acquired by the data acquisition module.
[0065] The scheme determination unit is used to pre-determine the optimal scheme for the deployment time and quantity of LNG storage facilities based on information such as delivery time, price and quantity provided by LNG liquefaction projects around the world, and to form the scheme with the lowest total cost (cargo purchase cost + transportation cost + storage cost + shortage cost).
[0066] The threshold setting unit is used to preset the price difference index threshold and the dynamic cost threshold.
[0067] The data processing unit is used to output a demand signal for LNG reserves when the LNG price difference index of the regional pipeline network is greater than the price difference index threshold, and to output a demand signal for LNG reserves when the dynamic cost data of the LNG storage facility is less than the dynamic cost threshold.
[0068] When the command issuing unit receives the LNG reserve demand signal from the liquid level sensor, the LNG reserve demand signal from the pressure sensor, or the LNG reserve demand signal output by the data processing unit, it issues a release command to the LNG storage facility action module.
[0069] The evaluation unit is used to periodically evaluate operations such as resource allocation and acquisition within a certain time period based on actual needs. The evaluation includes economic analysis, external market price change analysis, and social impact analysis of the operation.
[0070] Specifically, level sensors collect level signals from the storage tanks of each LNG receiving terminal within the LNG storage facility. The level indicates the amount of LNG stored in the facility. When the LNG reserve is sufficient, the facility can provide enough LNG when needed, according to a predetermined release rate, thereby achieving the goal of ensuring natural gas supply. When the LNG reserve is insufficient, the level sensors send a demand signal for LNG reserves to the LNG storage facility's decision-making module.
[0071] Specifically, pressure sensors collect pressure signals at the corresponding distribution stations. When a local area experiences gas shortages, the pipeline pressure signal drops. If the collected pressure signal is lower than a preset pressure threshold, a demand signal for LNG reserves is sent to the LNG storage facility decision module. If the pressure signal is greater than or equal to the preset pressure threshold, even if the LNG reserves are sufficient, LNG will not be released into the regional pipeline network to avoid impacting the local pipeline network.
[0072] Specifically, the LNG price difference index is mainly formed by the difference between the local natural gas market price in the regional pipeline network and the historical price for the same period, as well as the difference between the local natural gas price and the natural gas market price in the surrounding areas. This index measures the degree of local gas supply tightness from the perspective of market competition.
[0073] Specifically, dynamic cost data includes reference facility construction costs, operation and maintenance costs, and resource procurement costs (market repurchase value).
[0074] Example 2
[0075] like Figure 2 As shown, this embodiment provides a method for releasing LNG reserves, including the following steps:
[0076] 1) A corresponding liquid level sensor is installed at each LNG receiving station storage tank in each LNG storage facility, and a corresponding pressure sensor is installed at each distribution station of the pipeline network in the area covered by the LNG storage facility.
[0077] 2) The LNG storage facility decision-making module periodically sends out data collection demand signals.
[0078] 3) The data acquisition module obtains the LNG price difference index of the pipeline network in the area covered by the LNG storage facility and the dynamic cost data of the LNG storage facility in real time based on the data acquisition demand signals periodically issued by the LNG storage facility decision module, and sends them to the LNG storage facility decision module.
[0079] 4) The LNG storage facility decision-making module determines the release time and quantity of LNG storage facilities.
[0080] 5) Each level sensor collects the level signal of the corresponding LNG receiving station tank in the LNG storage facility in real time based on the data acquisition request signal periodically issued by the LNG storage facility decision module; each pressure sensor collects the pressure signal at the corresponding distribution station in real time based on the data acquisition request signal periodically issued by the LNG storage facility decision module.
[0081] 6) When the liquid level signal collected by the liquid level sensor is less than the preset liquid level threshold, the demand signal for LNG storage quantity is output to the LNG storage facility decision module.
[0082] 7) When the liquid level signal collected by the liquid level sensor is not less than the preset liquid level threshold and the pressure signal collected by the pressure sensor is less than the preset pressure threshold, the demand signal for LNG storage quantity is output to the LNG storage facility decision module.
[0083] 8) The LNG storage facility decision-making module, based on the LNG storage demand signals from the level sensor and pressure sensor, the LNG price difference index of the regional pipeline network, or the dynamic cost data of the LNG storage facility, issues a release instruction to the LNG storage facility action module, specifically:
[0084] 8.1) The LNG storage facility decision-making module pre-sets the price difference index threshold and the dynamic cost threshold.
[0085] 8.2) When the pressure signal collected by the pressure sensor is not less than the preset pressure threshold and the LNG price difference index of the regional pipeline network is greater than the price difference index threshold, the demand signal for LNG reserves is output.
[0086] 8.3) When the LNG price difference index of the regional pipeline network is not greater than the price difference index threshold and the dynamic cost data of the LNG storage facility is less than the dynamic cost threshold, output the demand signal for LNG storage volume; otherwise, maintain the status quo and form a cyclical LNG release decision.
[0087] 8.4) The LNG storage facility decision-making module issues a release instruction to the LNG storage facility action module based on the demand signal of LNG storage volume.
[0088] 9) The LNG storage facility operation module controls the LNG storage facility to release a predetermined amount of LNG into the regional pipeline network at a predetermined release time, based on the release command issued.
[0089] 10) The LNG storage facility decision-making module also periodically evaluates operations such as resource deployment and acquisition within a certain time period based on actual needs.
[0090] The above embodiments are only used to illustrate the present invention. The structure, connection method and manufacturing process of each component can be varied. All equivalent transformations and improvements made on the basis of the technical solution of the present invention should not be excluded from the protection scope of the present invention.
Claims
1. An LNG storage and delivery system, characterized in that, This includes a level sensor, a pressure sensor, a data acquisition module, an LNG storage facility decision-making module, and an LNG storage facility operation module; The liquid level sensor is used to collect the liquid level signal of the corresponding LNG receiving station storage tank in the LNG storage facility in real time. When the collected liquid level signal is less than the preset liquid level threshold, it outputs the demand signal of LNG storage quantity. The pressure sensor is used to collect the pressure signal at the corresponding distribution station in real time. When the collected pressure signal is less than the preset pressure threshold, it outputs the LNG reserve demand signal. The data acquisition module is used to acquire in real time the LNG price difference index of the pipeline network in the area covered by the LNG storage facility and the dynamic cost data of the LNG storage facility. The LNG storage facility decision module is used to determine the release time and release quantity of the LNG storage facility, and to issue release instructions based on the LNG storage quantity demand signal sent by the liquid level sensor, the LNG storage quantity demand signal sent by the pressure sensor, the LNG price difference index of the regional pipeline network, or the dynamic cost data of the LNG storage facility. The LNG storage facility operation module is used to control the LNG storage facility to release a determined amount of LNG into the regional pipeline network at a determined release time, according to the release instruction issued. The LNG storage facility decision-making module is equipped with: The data acquisition unit is used to acquire the demand signal of LNG reserves sent by the liquid level sensor or pressure sensor, as well as the LNG price difference index and dynamic cost data acquired by the data acquisition module. The scheme determination unit is used to pre-determine the release time and quantity of LNG storage facilities; The threshold setting unit is used to preset the price difference index threshold and the dynamic cost threshold; The data processing unit is used to output a demand signal for LNG reserves when the LNG price difference index of the regional pipeline network is greater than the price difference index threshold, and to output a demand signal for LNG reserves when the dynamic cost data of the LNG storage facility is less than the dynamic cost threshold. When the instruction issuing unit receives the LNG reserve demand signal from the liquid level sensor, the LNG reserve demand signal from the pressure sensor, or the LNG reserve demand signal output by the data processing unit, it issues a release instruction to the LNG storage facility operation module.
2. The LNG storage and delivery system as described in claim 1, characterized in that, Several of the liquid level sensors are fixedly installed at the corresponding LNG receiving station storage tanks within the corresponding LNG storage facilities, and several of the pressure sensors are fixedly installed at the corresponding distribution stations of the pipeline network covering the area of the LNG storage facilities.
3. The LNG storage and delivery system as described in claim 1, characterized in that, The data acquisition operations of the liquid level sensor, pressure sensor, and data acquisition module are all based on the data acquisition demand signals periodically issued by the LNG storage facility decision module.
4. The LNG storage and delivery system as described in claim 1, characterized in that, The LNG storage facility decision-making module is also equipped with: The demand signal transmission unit is used to periodically output data acquisition demand signals to the liquid level sensor, pressure sensor and data acquisition module.
5. An LNG storage and delivery system as described in claim 1, characterized in that, The LNG storage facility decision-making module is also equipped with: The evaluation unit is used to periodically evaluate the resource allocation and acquisition operations within a certain time period based on actual needs.
6. An LNG storage and delivery method based on an LNG storage and delivery system according to any one of claims 1 to 5, characterized in that, include: The data acquisition module obtains in real time the LNG price difference index of the pipeline network in the area covered by the LNG storage facility and the dynamic cost data of the LNG storage facility; The LNG storage facility decision-making module determines the timing and quantity of LNG release from the storage facility; Each level sensor collects the level signal of the corresponding LNG receiving station tank in the LNG storage facility in real time, and each pressure sensor collects the pressure signal of the corresponding distribution station in real time. When the liquid level signal collected by the liquid level sensor is lower than the preset liquid level threshold, the demand signal for LNG storage is output to the LNG storage facility decision module. When the liquid level signal collected by the liquid level sensor is not less than the preset liquid level threshold and the pressure signal collected by the pressure sensor is less than the preset pressure threshold, the demand signal for LNG storage quantity is output to the LNG storage facility decision module. The LNG storage facility decision-making module issues a release instruction to the LNG storage facility action module based on the LNG storage demand signal sent by the level sensor, the LNG storage demand signal sent by the pressure sensor, the LNG price difference index of the regional pipeline network, or the dynamic cost data of the LNG storage facility. The LNG storage facility operation module controls the LNG storage facility to release a predetermined amount of LNG into the regional pipeline network at a predetermined release time, based on the release command issued.
7. The LNG reserve release method as described in claim 6, characterized in that, The method also includes: A corresponding liquid level sensor is installed at each LNG receiving station storage tank within each LNG storage facility, and a corresponding pressure sensor is installed at each distribution station of the pipeline network covering the LNG storage facility area.
8. The LNG reserve release method as described in claim 6, characterized in that, The method also includes: The LNG storage facility decision-making module periodically sends out data collection request signals; The data acquisition work of the level sensor, pressure sensor, and data acquisition module is all based on this data acquisition requirement signal.
9. The LNG reserve release method as described in claim 6, characterized in that, The LNG storage facility decision-making module, based on the LNG storage demand signals from the level sensor, the pressure sensor, the regional pipeline LNG price difference index, or the dynamic cost data of the LNG storage facility, issues a release instruction to the LNG storage facility action module, including: The LNG storage facility decision-making module pre-sets price difference index thresholds and dynamic cost thresholds; When the pressure signal collected by the pressure sensor is not less than the preset pressure threshold and the LNG price difference index of the regional pipeline network is greater than the price difference index threshold, the demand signal for LNG reserves is output. When the LNG price difference index of the regional pipeline network is not greater than the price difference index threshold and the dynamic cost data of the LNG storage facilities is less than the dynamic cost threshold, a demand signal for LNG storage volume is output; otherwise, the status quo is maintained. The LNG storage facility decision-making module issues a release instruction to the LNG storage facility action module based on the demand signal for LNG storage volume.
Citation Information
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